Making multi-axis methods feasible for multi-omics data

Multi-axis models are a promising technique for simultaneously producing information about all ‘axes’ in a dataset under modest assumptions. For single cell RNA-sequencing data, they learn gene and cell ‘conditional dependency’ networks. However, the applicability of such models is limited due to their inability to handle multi-modal datasets and poor scalability: they can only run on datasets with thousands of cells/genes, whereas modern datasets have 20,000-30,000 genes, millions of cells, and potentially additional modalities such as ATAC-seq. In this thesis, we increase the scalability of such models to millions of cells, and verify this by applying our methodology to one such million-cell dataset. We also generalize the model to multi-modal datasets. Finally, we investigate the assumptions underpinning these models and apply our techniques to learn causal networks. In particular, we demonstrate how to relax the zero mean assumption to a ‘Kronecker-sum-structured mean’ assumption, how to relax the Cartesian product assumption common in multi-axis models, and finally how to relax the Gaussian assumption, by generalizing multi-axis methodologies to the family of elliptical distributions. These relaxations are built on top of GmGM, and in particular rely on its scalability; they would not be feasible without the scalability work we undertook.